CAT 1995 — QA Question 46
Directions for next 4 questions: Answer the questions based on the following information.
le(x, y) = Least of (x, y)
mo(x) = |x|
me(x, y) = Maximum of (x, y)
Direction: Each of these questions is followed by two statements, I and II. Mark the answer as
1. if the question can be answered with the help of statement I alone.
2. if the question can be answered with the help of statement II alone.
3. if both statement I and statement II are needed to answer the question.
4. if the question cannot be answered even with the help of both the statements.
What is the first term of an arithmetic progression of positive integers?
I. Sum of the squares of the first and the second term is 116.
II. The fifth term is divisible by 7.
Answer & solution
Answer: 1
Since 116 is less than 112, it can be figured out that both the first two terms of the AP should be less than 10.
There is only one pair of positive integers whose squares add up to 116 and they are 10 and 4.
Thus, these two should be the first two terms of the AP.
Hence, the first term is 4, and can be obtained only from statement I.
Statement II merely suggests that the fifth term is of the form 7k. Nothing correct can be concluded from this.